The MSX was indeed capable of I/O through the joystick ports, because they were driven by the AY3-8910 PSG's I/O ports. In the ZX Spectrum, there were several interface standards but all were only capable of reading (input) from, not writing to the joystick port(s).

In the ZX Spectrum Next, the joystick ports are driven from FPGA pins so theoretically bidirectional I/O is possible, but unless you modify it yourself, the current Core is based on legacy (input-only) standards, with the newly added feature of driving two SELECT pins high or low, so yes you can certainly repurpose these pins (1 in each joy port) as output lines, and develop something similar to the bit-banged RS-232 serial interfaces throug the joystick ports that alreaady exist for the MSX.

Finally, remember that if a serial interface can meet your need, the ZX Next also have two powerful serial interfaces built-in: I2C (used on the RTC interface) and SPI (used by the SD storage and Raspberry Pi interfaces).

But if you really need a 8 or 16 bit parallel interface (as you first mentioned), it's still easier to use an external device on the Expansion Bus where you have access to the Z80 address and control lines.

Supports Sega Megadrive 3 (and 6) button Joypads. Currently 4 buttons can be used at maximum. The buttons are returned by reading the Kempston joystick ports (IN 31 / IN 55). Sega 6 XYZ buttons are mirrored on ABC.

The following register has been updated to include these extra joypad modes.(R/W) 0x05 (05) => Peripheral 1 setting

In the article, it was written that if you set the joystick mode to "MD1" "MD2", MD's "6 button pad" can be used with SpectrumNext.
But it is written with a maximum of 4 buttons. The expression "mirrored" means that six buttons arranged in two groups can be read as three buttons, but it means "you can not specify a group to read".

Although "Next Joystick Port" can specify the type of joystick with the control register, it seems that it will be replaced internally and used as a Kempston interface. Similarly for PS/2 port.

Therefore, my hope of "if there is an output terminal even with 1 pin" has disappeared.

Finally, remember that if a serial interface can meet your need, the ZX Next also have two powerful serial interfaces built-in: I2C (used on the RTC interface) and SPI (used by the SD storage and Raspberry Pi interfaces).

But if you really need a 8 or 16 bit parallel interface (as you first mentioned), it's still easier to use an external device on the Expansion Bus where you have access to the Z80 address and control lines.

Have fun

Parallel port communication is used for devices that send 8-bit register data.
PSG or OPLL(YM2413, YMF281, etc.) works just by sending a register number and data at a certain timing. I saw a demonstration to convert 4bit output to 8bit output with D-flop circuit. I wanted to make an inexpensive FM Sound device.

If there is an output port even with 1 bit, serial communication can be performed by software, and it can be used as a MIDI output port or controlling an external microcomputer.

If the SPI communication port is available, we can connect "ATTiny etc's microcomputer" to make FIFO control and create a MIDI I/O interface. Moreover, it may be possible to control equipment by connecting "Parallel IO Expander IC".
If the signal of the pin is decoded directly to the IO port, we can use it also in "handshake communication". For example, can we retrieve an 8-bit parallel output with shift register IC (74HC164)?